Chapter 9.4, Problem 22E

(a)

To determine

To calculate: To sketch the curve represented by the parametric equations

Explanation of Solution

Given information: Parametric equations $x=\left|t-1\right|;y=t+2$

Calculation:

Parametric equations are given as

  $x=\left|t-1\right|;y=t+2$

Calculating the values of $x$ and $y$ at various values of $t$

$t$	$x$	$y$
-3	-4	1
-2	-3	0
-1	-2	1
0	-1	2
1	0	3
2	1	4
3	2	5

Graph of the function is as follows:

The arrows on the curve indicates its orientation as $t$ increases from $-3$ to $3$

  

Conclusion:

Hence, graph is sketched

(b)

To determine

To calculate: To write the rectangular equations for the parametric equations

Answer to Problem 22E

The rectangular equation is $x=\left|y-3\right|$

Explanation of Solution

Given information: Parametric equations $x=\left|t-1\right|;y=t+2$

Calculation:

Parametric equations are given as

  $x=\left|t-1\right|;y=t+2$

From equation $y=t+2$

  $\begin{array}{l}y=t+2\\ t=y-2----(1)\end{array}$

Substitute $t=y-2$ in $x=\left|t-1\right|$ ,

  $\begin{array}{l}y=\left|\frac{x}{2}-2\right|\\ 2y=\left|x-4\right|\end{array}$

Here, domain is $0<t<\infty$

Conclusion:

Hence, rectangular equation is $x=\left|y-3\right|$